Hybridization of the Univariate Marginal Distribution Algorithm with Simulated Annealing for Parametric Parabola Detection

  • S. Ivvan Valdez
  • Susana Espinoza-Perez
  • Fernando Cervantes-Sanchez
  • Ivan Cruz-AcevesEmail author


This chapter presents a new hybrid optimization method based on the univariate marginal distribution algorithm for a continuous domain, and the heuristic of simulated annealing for the parabola detection problem. The hybrid proposed method is applied to the DRIVE database of retinal fundus images to approximate the retinal vessels as a parabolic shape. The hybrid method is applied separately using two different objective functions. Firstly, the objective function only considers the superposition of pixels between the target pixels in the input image and the virtual parabola; secondly, the objective function implements a weighted restriction on the pixels close to the parabola vertex. Both objective functions in the hybrid method obtain suitable results to approximate a parabolic form on the retinal vessels present in the retinal images. The experiments show that the parabola detection results obtained from the proposed method are more robust than those obtained by the comparative method. Additionally, the average execution time achieved by the proposed hybrid method (1.57 s) is lower than the computational time obtained by the comparative method on the database of 20 retinal images, which is of interest to computer-aided diagnosis in clinical practice.


Estimation of distribution algorithms Hough transform Hybrid optimization Image analysis Parabola detection Simulated annealing 



This research was supported by the National Council of Science and Technology of México under the project: Cátedras-CONACYT 3150-3097.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • S. Ivvan Valdez
    • 1
  • Susana Espinoza-Perez
    • 2
  • Fernando Cervantes-Sanchez
    • 3
  • Ivan Cruz-Aceves
    • 4
    Email author
  1. 1.División de IngenieríasUniversidad de GuanajuatoSalamancaMexico
  2. 2.Universidad del Papaloapan, Ingeniería en ComputaciónLoma BonitaMexico
  3. 3.Centro de Investigación en Matemáticas (CIMAT)ValencianaMexico
  4. 4.CONACYT, Centro de Investigación en Matemáticas (CIMAT)ValencianaMexico

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